Step 1: Preheat your oven to 400°F (200°C) and line a large baking sheet with parchment paper for easy cleanup.
Step 2: Grate the zucchini using a fine grater. Place the grated zucchini in a clean kitchen towel or cheesecloth and squeeze firmly over the sink to remove as much moisture as possible.
Step 3: In a large mixing bowl, combine the ground meat, squeezed zucchini, breadcrumbs, egg, minced garlic, Italian seasoning, salt, and pepper.
Step 4: Mix the ingredients by hand until just combined, being careful not to overwork the meat. Shape the mixture into approximately 16-20 meatballs.
Step 5: Place the meatballs on the prepared baking sheet and bake for 18-20 minutes, or until they are browned and reach an internal temperature of 165°F.
Step 6: While the meatballs bake, slice the sub rolls and toast them lightly in the oven or a toaster. Spread a small amount of marinara sauce on the bottom of each roll.
Step 7: Place 4-5 meatballs into each roll, top with remaining marinara sauce and a generous sprinkle of mozzarella cheese.
Step 8: Place the assembled subs back into the oven under the broiler for 1-2 minutes, or until the cheese is melted and bubbly. Garnish with parsley and serve immediately.